We consider a two-dimensional transport equation subject to small diffusive perturbations. The transport equation is given by a Hamiltonian flow near a compact and connected heteroclinic cycle. We investigate approximately harmonic functions corresponding to the generator of the perturbed transport equation. In particular, we investigate such functions in the boundary layer near the heteroclini...

On a Riemannian manifold, a solution of the Killing equation is an infinitesimal isometry. Since the Killing equation is overdetermined, infinitesimal isometries do not exist in general. The complete prolongation of the Killing equation is a PDE on the bundle of 1-jets of vector fields. Restricted to a curve, it becomes an ODE that generalizes the Jacobi equation. A solution of this ODE is call...

Catchment-scale chemical transport is jointly controlled by hydrological and chemical processes. Water may take a complex set of flowpaths underground toward the stream, carrying soluble substances with it. Some chemical constituents are nonreactive; these act as passive tracers, moving with the water. Other constituents react with the porous medium; concentrations of these reactive tracers rev...

Solute mass transport in porous media is strongly correlated with pore fluid flow. The analysis of solute transport is an effective means for studying medium heterogeneities. In this study, we discuss the effects of heterogeneity on the tracer transport. Assuming steady fluid flow, we have simulated tracer transport in various permeability heterogeneities. The results show that the tracer distr...

Rui M. R. de Bastos SUPERPOSITION RENDERING: Increased Realism for Interactive Walkthroughs (Under the direction of Dr. Frederick P. Brooks, Jr.) The light transport equation, conventionally known as the rendering equation in a slightly different form, is an implicit integral equation, which represents the interactions of light with matter and the distribution of light in a scene. This research...

Rui M. R. de Bastos SUPERPOSITION RENDERING: Increased Realism for Interactive Walkthroughs (Under the direction of Dr. Frederick P. Brooks, Jr.) The light transport equation, conventionally known as the rendering equation in a slightly different form, is an implicit integral equation, which represents the interactions of light with matter and the distribution of light in a scene. This research...